What process powers the movement of tectonic plates?

Its more than just the movement of magma. Its called continental drift.
continental drift
A theory stating that the Earth's continents have been joined together and have moved away from each other at different times in the Earth's history. The theory was first proposed by Alfred Wegener in 1912. While his general idea of continental movement eventually became widely accepted, his explanation for the mechanism of the movement has been supplanted by the theory of plant tectonics. See more at plate tectonics.